Solid-State Physics: An Introduction to Principles of Materials Science

SMART ELECTRONIC MATERIALS

Smart materials respond rapidly to external stimuli to alter their physical properties.

They are used in devices that are driving advances in modern information technol￾ogy and have applications in electronics, optoelectronics, sensors, memories and

other areas.

This book fully explains the physical properties of these materials, including

semiconductors, dielectrics, ferroelectrics, and ferromagnetics. Fundamental con￾cepts are consistently connected to their real-world applications. It covers structural

issues, electronic properties, transport properties, polarization-related properties,

and magnetic properties of a wide range of smart materials.

The book contains carefully chosen worked examples to convey important con￾cepts and has many end-of-chapter problems.

It is written for first year graduate students in electrical engineering, material

sciences, or applied physics programs. It is also an invaluable book for engineers

working in industry or research laboratories. A solution manual and a set of useful

viewgraphs are also available for instructors by visiting http://www.cambridge.org/

0521850274.

JASPRIT SINGH obtained his Ph.D. in Solid State Physics from the University of

Chicago. He is currently a professor in the Applied Physics Program and in the

Department of Electronic and Computer Science at the University of Michigan,

Ann Arbor. He has held visiting positions at the University of California in Santa

Barbara. He has authored over 250 technical articles. He has also authored eight

textbooks in the area of applied physics and technology. His area of expertise is

novel materials for applications in intelligent devices.

SMART ELECTRONIC MATERIALS

Fundamentals and Applications

JASPRIT SINGH

University of Michigan

CAMBRIDGE

UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo

Cambridge University Press

The Edinburgh Building, Cambridge CB2 2RU, UK

www.cambridge.org

Information on this title: www.cambridge.org/9780521850274

© Cambridge University Press 2005

This book is in copyright. Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without

the written permission of Cambridge University Press.

First published 2005

Printed in the United Kingdom at the University Press, Cambridge

A catalog record for this book is available from the British Library

Library of Congress Cataloging in Publication data

ISBN-13 978-0-521 -85027-4 hardback

ISBN-10 0-521 -85027-4 hardback

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or

third-party internet websites referred to in this book, and does not guarantee that any content on such websites is,

or will remain, accurate or appropriate.

CONTENTS

1

PREFACE page xi

INTRODUCTION xiii

1 SMART MATERIALS: AN INTRODUCTION xiii

2 INPUT—OUTPUT DECISION ABILITY xiv

2.1 Device based on conductivity changes xiv

2.2 Device based on changes in optical response xv

3 BIOLOGICAL SYSTEMS: NATURE'S SMART MATERIALS xix

4 ROLE OF THIS BOOK xxii

STRUCTURAL PROPERTIES 1

1.1 INTRODUCTION 1

1.2 CRYSTALINE MATERIALS 1

1.2.1 Basic lattice types 2

1.2.2 Some important crystal structures 5

1.2.3 Notation to denote planes and points in a lattice:

Miller indices 12

1.2.4 Artificial structures: superlattices and quantum wells 16

1.2.5 Surfaces: ideal versus real 17

1.2.6 Interfaces 19

1.3 DEFECTS IN CRYSTALS 20

1.4 HETEROSTRUCTURES 23

1.5 NON-CRYSTALLINE MATERIALS 24

1.5.1 Polycrystalline materials 25

1.5.2 Amorphous and glassy materials 26

1.5.3 Liquid crystals 27

1.5.4 Organic materials 31

1.6 SUMMARY 31

vi Contents

1.7 PROBLEMS 33

1.8 FURTHER READING 37

2 QUANTUM MECHANICS AND

ELECTRONIC LEVELS 39

2.1 INTRODUCTION 39

2.2 NEE D FOR QUANTUM DESCRIPTION 40

2.2.1 Some experiments that ushered in the quantum age 40

2.3 SCHRODINGER EQUATION AND PHYSICAL OBSERVABLES 48

2.3.1 .Wave amplitude 52

2.3.2 Waves, wavepackets, and uncertainty 54

2.4 PARTICLES IN AN ATTRACTIVE POTENTIAL: BOUND STATES 57

2.4.1 Electronic levels in a hydrogen atom 58

2.4.2 Particle in a quantum well 62

2.4.3 Harmonic oscillator problem 67

2.5 FROM ATOMS TO MOLECULES: COUPLED WELLS 69

2.6 ELECTRONS IN CRYSTALLINE SOLIDS 77

2.6.1 Electrons in a uniform potential 80

2.6.2 Particle in a periodic potential: Bloch theorem 85

2.6.3 Kronig-Penney model for bandstructure 87

2.7 SUMMARY 93

2.8 PROBLEMS 93

2.9 FURTHER READING 99

U ELECTRONIC LEVELS IN SOLIDS 100

3.1 INTRODUCTION 100

3.2 OCCUPATION OF STATES: DISTRIBUTION FUNCTION 100

3.3 METALS, INSULATORS, AND SUPERCONDUCTORS 104

3.3.1 Holes in semiconductors 104

3.3.2 Bands in organic and molecular semiconductors 107

3.3.3 Normal and superconducting states 108

3.4 BANDSTRUCTURE OF SOME IMPORTANT SEMICONDUCTORS 110

3.4.1 Direct and indirect semiconductors: effective mass 111

Contents VII

3.5 MOBILE CARRIERS 116

3.5.1 Electrons in metals 117

3.5.2 Mobile carriers in pure semiconductors 120

3.6 DOPING OF SEMICONDUCTORS 126

3.7 TAILORING ELECTRONIC PROPERTIES 131

3.7.1 Electronic properties of alloys 131

3.7.2 Electronic properties of quantum wells 132

3.8 LOCALIZED STATES IN SOLIDS 136

3.8.1 Disordered materials: extended and localized states 138

3.9 SUMMARY 141

3.10 PROBLEMS 141

3.11 FURTHER READING 146

CHARGE TRANSPORT IN MATERIALS 148

4.1 INTRODUCTION 148

4.2 AN OVERVIEW OF ELECTRONIC STATES 149

4.3 TRANSPORT AND SCATTERING 151

4.3.1 Scattering of electrons 154

4.4 MACROSCOPIC TRANSPORT PROPERTIES 162

4.4.1 Velocity-electric field relations in semiconductors 162

4.5 CARRIER TRANSPORT BY DIFFUSION 173

4.5.1 Transport by drift and diffusion: Einstein's relation 175

4.6 IMPORTANT DEVICES BASED ON CONDUCTIVITY CHANGES 178

4.6.1 Field effect transistor 179

4.6.2 Bipolar junction devices 184

4.7 TRANSPORT IN NON-CRYSTALLINE MATERIALS 186

4.7.1 Electron and hole transport in disordered systems 187

4.7.2 Ionic conduction 191

4.8 IMPORTANT NON-CRYSTALLINE ELECTRONIC DEVICES 193

4.8.1 Thin film transistor 193

4.8.2 Gas sensors 195

4.9 SUMMARY 195

4.10 PROBLEMS 199

4.11 FURTHER READING 200

VIII Contents

LIGHT ABSORPTION AND EMISSION 202

5.1 INTRODUCTION 202

5.2 IMPORTANT MATERIAL SYSTEMS 204

5.3 OPTICAL PROCESSES IN SEMICONDUCTORS 207

5.3.1 Optical absorption and emission 210

5.3.2 Chargei injection, quasi-Fermi levels, and recombination 219

5.3.3 Optical absorption, loss, and gain 225

5.4 OPTICAL PROCESSES IN QUANTUM WELLS 226

5.5 IMPORTANT SEMICONDUCTOR OPTOELECTRONIC DEVICES 231

5.5.1 Light detectors and solar cells 231

5.5.2 Light emitting diode 238

5.5.3 Laser diode 243

5.6 ORGANIC SEMICONDUCTORS: OPTICAL PROCESSES & DEVICES 251

5.6.1 Excitonic state 252

5.7 SUMMARY 255

5.8 PROBLEMS 255

5.9 FURTHER READING 262

DIELECTRIC RESPONSE: POLARIZATION EFFECTS 264

6.1 INTRODUCTION 264

6.2 POLARIZATION IN MATERIALS: DIELECTRIC RESPONSE 265

6.2.1 Dielectric response: some definitions 265

6.3 FERROELECTRIC DIELECTRIC RESPONSE 273

6.4 TAILORING POLARIZATION: PIEZOELECTRIC EFFECT 275

6.5 TAILORING POLARIZATION: PYROELECTRIC EFFECT 285

6.6 DEVICE APPLICATIONS OF POLAR MATERIALS 287

6.6.1 Ferroelectric memory 287

6.6.2 Strain sensor and accelerometer 288

6.6.3 Ultrasound generation 289

6.6.4 Infrared detection using pyroelectric devices 289

Contents

6.7 SUMMARY 291

6.8 PROBLEMS 291

6.9 FURTHER READIN G 295

OPTICAL MODULATION AND SWITCHING 296

7.1 INTRODUCTION 296

7.2 LIGHT PROPAGATION IN MATERIALS 297

7.3 MODULATION OF OPTICAL PROPERTIES 302

7.3.1 Electro-optic effect 303

7.3.2 Electro-absorption modulation 309

7.4 OPTICAL MODULATION DEVICES 312

7.4.1 Electro-optic modulators 316

7.4.2 Interferroelectric modulators 318

7.5 SUMMARY 323

7.6 PROBLEMS 325

7.7 FURTHER READING 325

MAGNETIC EFFECTS IN SOLIDS 326

8.1 INTRODUCTION 326

8.2 MAGNETIC MATERIALS 326

8.3 ELECTROMAGNETIC FIELD MAGNETIC MATERIALS 327

8.4 PHYSICAL BASIS FOR MAGNETIC PROPERTIES 331

8.5 COHERENT TRANSPORT: QUANTUM INTERFERENCE 335

8.5.1 Aharonov Bohm effect 335

8.5.2 Quantum interference in superconducting materials 338

8.6 DlAMAGNETIC AND PARAMAGNETIC EFFECTS 340

8.6.1 Diamagnetic effect 340

8.6.2 Paramagnetic effect 341

8.6.3 Paramagnetism in the conduction electrons in metals 345

A

B

C

D

E

Contents

8.7 FERROMAGNETIC EFFECTS 346

8.7.1 Exchange interaction and ferromagnetism 346

8.7.2 Antiferromagnetic ordering 348

8.8 APPLICATIONS IN MAGNETIC DEVICES 352

8.8.1 Quantum interference devices 352

8.8.2 Application example: cooling by demagnetization 354

8.8.3 Magneto-optic modulators 355

8.8.4 Application example: magnetic recording 357

8.8.5 Giant magnetic resistance (GMR) devices 359

8.9 SUMMARY 359

8.10 PROBLEMS 359

8.11 FURTHER READING 362

IMPORTANT PROPERTIES

OF SEMICONDUCTORS 363

P-N DIODE: A SUMMARY 368

B.1 INTRODUCTION 368

B.2 P-N JUNCTION 368

B.2.1 P-N Junction under bias 372

FERMI GOLDEN RULE 380

LATTICE VIBRATIONS AND PHONONS 386

DEFECT SCATTERING AND MOBILITY 393

E.1 ALLOY SCATTERING 393

E.2 SCREENED COULOMBIC SCATTERING 396

E.3 IONIZED IMPURITY LIMITED MOBILITY 400

E.4 ALLOY SCATTERING LIMITED MOBILITY 402

INDEX 404

PREFACE

Semiconductor-based devices such, as transistors and diodes enabled technologies that

have ushered in the information age. Computation, communication, storage, and display

have all been impacted by semiconductors. The importance of semiconductors is recog￾nized if we examine the number of undergraduate and graduate courses that cater to the

physics and devices based on these materials. In nearly all electrical engineering depart￾ments there are one to two undergraduate courses on the general topic of "physics of

semiconductor devices." There are similarly two to three courses in graduate programs

on semiconductor physics and devices. In many materials science departments and in

physics (or applied physics) departments there are one or two courses where the focus

is on semiconductors.

Semiconductors have achieved dominance in information technology because it

is possible to rapidly alter their conductivity and optical properties. However, there are

other materials that can also rightfully claim to be "smart." New applications and needs

are now making these other materials increasingly important. Devices that are usually

called sensors or actuators are based on ceramics or insulators which have some prop￾erties that traditional semiconductors cannot match. Similarly, organic polymers can

provide low-cost alternatives to traditional semiconductors in areas like image display,

solar energy conversion, etc.

Increasingly we have to view intelligent devices as being made from a wide

variety of materials - semiconductors, piezoelectric materials, pyroelectric materials,

ferroelectrics, ferromagnetics, organic semiconductors, etc. Currently some electrical

engineering departments and some materials science departments offer courses on "sen￾sors and actuators" or "ceramics." Some physics departments also offer courses on gen￾eral "solid state physics," which cover some aspects of ceramics. In this book I have

attempted to offer material where "traditional" semiconductors, "traditional" smart ce￾ramics, and newly emerging organic semiconductors are discussed in a coherent manner.

The book covers structural issues, electronic properties, transport properties, polarization￾related properties, and magnetic properties of a wide range of smart materials. We also

discuss how these properties are exploited for device applications.

This book is written for first year graduate students in an electrical engineering,

material science, or applied physics program.

I am grateful to my editor, Phil Meyler, for his support and encouragement.

The design, figures, and layout of the book was done by Teresa Singh, my wife. She also

provided the support without which this book would not be possible.

JASPRIT SINGH

Ann Arbor, MI

XI

INTRODUCTION

1.1 SMART MATERIALS: AN INTRODUCTION

Humans have used smart materials - materials that respond to input with a well-defined

output - for thousands of years. The footprint on a soft trail in a jungle can tell a well￾trained human (and almost all wild animals) what kind of animal recently passed and

even how much it weighed. In this case the soft mud acts as a smart material - responding

to and storing information about a passing animal. A reader of Sherlock Holmes is

undoubtedly familiar with all kinds of information stored in intelligent materials that

the clever detective was able to exploit. Over the last couple of decades the role of

smart materials in our lives has become so widespread that (at least, in the industrial

countries) most of us would be lost without these materials guiding us.

Let us follow Mr. XYZ (of course, it could also be a Ms. XYZ), a super salesman

for a medical supplies company, as he gets up one morning and goes about his business.

He checks his schedule on his laptop (semiconductor-based devices process the infor￾mation, liquid crystals help display the information, ferromagnetic- and polymer-based

materials store the information, a laser using semiconductors reads the information...).

Mr. XYZ sees that he has to catch a flight in an hour to make a presentation. As he

drives to the airport he sees on his car map that there is an accident on his normal

route. The car computer hooked up to a satellite system gives him an alternate route,

which gets him to the airport on time.

On the way to the terminal he has used a smart parking ticket on his cell phone.

As he goes through airport security he is scanned by a battery of machines, which

have used electromagnetic radiation of several frequencies, chemical sensors, ultrasound

images...

The airplane he takes is, of course, a marvel packed with smart materials -

sensors and computers fly most of the flight. Mr. XYZ deplanes and gets a rental car

with his credit card (another smart device). He makes a very successful presentation

with his smart audiovisual card, which he carries in his wallet. A dozen managers in

plants located all over the world also participate in the presentation.

As Mr. XYZ is heading back he falls and suffers a gash on his hand. It does

not look serious, but he stops by a clinic to have it checked. His health card is scanned,

giving the nurse a full history of his allergies, drugs he cannot take, current medication,

etc. His gash is patched up and he is given a pill, which will speed up the healing.

Mr. XYZ makes it safely to his home to enjoy a nice movie and some playtime

with his family.

Semiconductors, ferroelectrics, ferromagnetics, piezoelectrics, tailor-made poly￾mers - a plethora of smart materials have allowed Mr. XYZ to sail through the day. As

he sleeps soundly his two-year-old has a nightmare and screams out. He spends the rest

xm

xiv Introduction

of the night consoling the toddler. Although he does not have a smart technology that

will substitute for his hugs, perhaps after another 20 years...who knows!

In this book we will focus on the several classes of materials which have led

to modern information age devices. The list of materials being exploited for intelligent

devices is continuously increasing. However, there are certain common physical effects

that will form the underlying foundations for the materials we will examine.

1.2 INPUT-OUTPUT DECISION ABILITY

A key reason why some materials can be used in intelligent devices is the nature of

response that can be generated in some physical property of the device to input. For

example a voltage pulse applied across a copper wire does not produce a response (in

current) that can be used for digital or analog applications. However, a voltage pulse

across transistor made from silicon creates a response that can be exploited for intelligent

devices. Later in the book we will discuss what makes an input - output response usable

for decision making.

In Fig. 1 we show a typical input - output response in an intelligent device.

There are many other forms of the input - output relations that can be exploited for

decision making and we will discuss them later. In the response shown in Fig. 1 we

see that output has a "thresholding" behavior; i.e., it is low for a range of input and

then over a small range of input change it becomes high. This is a response that can be

exploited for "switching" applications or memory applications.

The input that a device may respond to may be an optical or a microwave sig￾nal, a poisonous gas, a pressure pulse (a sound pulse for example), an electrical voltage

pulse, etc. The output response also depends upon a wide range of physical phenomena

that alter the state of the device. The most commonly used physical phenomena for

smart devices are the following: (i) Conductivity changes or current flow in the device,

(ii) Optical properties that may involve light emission, light absorption, light amplifica￾tion, etc. The effects may involve changes in the refractive index, including absorption

coefficient or gain, of the material, (iii) Polarization changes. Many sensor technologies

exploit changes that occur in the polarization of a material when subjected to pressure

or strain or other inputs. The change in polarization produces a voltage change that

can be used to make decisions, (iv) Magnetization changes are exploited in technologies

such as a recording medium. In addition to these basic physical phenomena (charges)

there may be other changes such as temperature changes, volume changes, etc., which

can also be exploited for devices.

The materials that are used for modern information devices are varied and

complex and come from many different categories of solids. In Figs. 2 - 5 we show an

overview of the devices and materials that are driving the modern information age.

1.2.1 Devices based on conductivity changes

Devices that are based on materials where conductivity can be changed rapidly form

the bulk of modern information-processing devices. In Fig. 2 we show an overview of

the various devices, materials, and technologies that exploit changes in conductivity. As

1.2. Input-output decision ability xv

shown in the figure electronic transport in material can be incoherent or coherent. Most

present devices are based on incoherent transport, where the wave nature of electrons

(i.e., the quantum nature of electrons behaving as propagating waves with well-defined

phase coherence) is not exploited. Conductivity changes arise primarily due to an in￾crease or decrease in the number of current-carrying particles. Devices such as diodes

and field effect transistors that form the basis of modern semiconductor technology rely

on being able to alter conductivity rapidly by an input signal. Materials that have prop￾erties that allow large changes (up to orders of magnitude) in conductivity are usually

semiconductors, such as Si, Ge, GaAs, InP, etc. Recently organic materials have also

shown great promise.

Coherent transport devices

In classical physics, electrons, which are responsible for carrying current in solids, are

particles described by their mass, momentum, and position. In the more accurate quan￾tum description, the electrons are described by waves with a certain wavelength and

phase. In most cases, as electrons move in a solid, they suffer scattering, causing loss

of phase coherence. However, in very small devices as well as in superconductors, the

scattering is essentially absent and phase information is retained. In such cases, coher￾ent transport occurs and effects such as interference and diffraction can be exploited to

design devices.

As fabrication technologies improve, coherent transport-based devices will be￾come easier to fabricate for room temperature operation. At present such devices can

only operate at low temperatures. As shown in Fig. 2, such devices can be made from

semiconductors, metals, superconductors, etc.

1,2.2 Devices based on changes in optical response

The electromagnetic spectrum, in general, and visible light, in particular, are an impor￾tant part of the human experience. We use sight and sense (heat/cold) to survive and

thrive in nature. It is not surprising that technologies that involve generation or detec￾tion of light are very important. Optically active (i.e., optical properties can be altered)

materials form the basis of light emitters (for displays, optical communication, opti￾cal readout, publishing, etc.), light detectors (for imaging and coding/decoding), light

switches (for communication, image projection), and many other optical technologies,

such as medical diagnostics, crime scene analysis, etc.

A vast range of materials is used to design optical devices. These include tra￾ditional semiconductor polymers (such as GaAs, InGaAs, InN, and GaN).

Devices based on polar materials

There are a number of materials in which there is net polarization. The polarization

that causes a detectable electric field (or a voltage signal) can be exploited for a range

of applications. As shown in Fig. 4, several interesting physical phenomena involve

polarization effects. In ferroelectric materials the polarization can be altered by an

external electric field. The electric field-polarization relation shows a hysteresis curve,

so that the direction of polarization at a zero applied field can be switched. Such an

effect can be used for memory devices and is used widely for "smart cards." A number